LMFDB - Embedded newform 354.8.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$110.584299021$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 260588 x^{7} - 2627755 x^{6} + 16696953355 x^{5} + 808091684078 x^{4} + \cdots + 15\!\cdots\!00 $ x^9 - 4x^8 - 260588x^7 - 2627755x^6 + 16696953355x^5 + 808091684078x^4 - 191825159847522x^3 - 12153827093891319x^2 + 237398587398357570x + 15300107670464479800
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-415.350$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +33.0058 q^{5} +216.000 q^{6} +651.589 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +33.0058 q^{5} +216.000 q^{6} +651.589 q^{7} -512.000 q^{8} +729.000 q^{9} -264.046 q^{10} +6710.64 q^{11} -1728.00 q^{12} -3927.59 q^{13} -5212.71 q^{14} -891.156 q^{15} +4096.00 q^{16} -14088.6 q^{17} -5832.00 q^{18} -29214.8 q^{19} +2112.37 q^{20} -17592.9 q^{21} -53685.1 q^{22} +65810.5 q^{23} +13824.0 q^{24} -77035.6 q^{25} +31420.7 q^{26} -19683.0 q^{27} +41701.7 q^{28} -30949.5 q^{29} +7129.25 q^{30} -201373. q^{31} -32768.0 q^{32} -181187. q^{33} +112709. q^{34} +21506.2 q^{35} +46656.0 q^{36} +255543. q^{37} +233719. q^{38} +106045. q^{39} -16899.0 q^{40} -120712. q^{41} +140743. q^{42} +686859. q^{43} +429481. q^{44} +24061.2 q^{45} -526484. q^{46} -887083. q^{47} -110592. q^{48} -398975. q^{49} +616285. q^{50} +380393. q^{51} -251366. q^{52} -1.60047e6 q^{53} +157464. q^{54} +221490. q^{55} -333613. q^{56} +788801. q^{57} +247596. q^{58} +205379. q^{59} -57034.0 q^{60} +2.18882e6 q^{61} +1.61098e6 q^{62} +475008. q^{63} +262144. q^{64} -129633. q^{65} +1.44950e6 q^{66} +235145. q^{67} -901671. q^{68} -1.77688e6 q^{69} -172050. q^{70} +2.98582e6 q^{71} -373248. q^{72} -2.63695e6 q^{73} -2.04434e6 q^{74} +2.07996e6 q^{75} -1.86975e6 q^{76} +4.37258e6 q^{77} -848359. q^{78} +6.56186e6 q^{79} +135192. q^{80} +531441. q^{81} +965699. q^{82} +1.83037e6 q^{83} -1.12594e6 q^{84} -465006. q^{85} -5.49487e6 q^{86} +835635. q^{87} -3.43585e6 q^{88} +2.35466e6 q^{89} -192490. q^{90} -2.55917e6 q^{91} +4.21187e6 q^{92} +5.43707e6 q^{93} +7.09666e6 q^{94} -964259. q^{95} +884736. q^{96} +4.28818e6 q^{97} +3.19180e6 q^{98} +4.89206e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	33.0058	0.118085	0.0590426	−	0.998255i	$-0.481195\pi$
$5$	33.0058	0.118085	0.0590426	+	0.998255i	$0.481195\pi$
$6$	216.000	0.408248
$7$	651.589	0.718010	0.359005	−	0.933336i	$-0.383116\pi$
$7$	651.589	0.718010	0.359005	+	0.933336i	$0.383116\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−264.046	−0.0834988
$11$	6710.64	1.52016	0.760081	−	0.649829i	$-0.225159\pi$
$11$	6710.64	1.52016	0.760081	+	0.649829i	$0.225159\pi$
$12$	−1728.00	−0.288675
$13$	−3927.59	−0.495820	−0.247910	−	0.968783i	$-0.579744\pi$
$13$	−3927.59	−0.495820	−0.247910	+	0.968783i	$0.579744\pi$
$14$	−5212.71	−0.507709
$15$	−891.156	−0.0681765
$16$	4096.00	0.250000
$17$	−14088.6	−0.695500	−0.347750	−	0.937587i	$-0.613054\pi$
$17$	−14088.6	−0.695500	−0.347750	+	0.937587i	$0.613054\pi$
$18$	−5832.00	−0.235702
$19$	−29214.8	−0.977161	−0.488580	−	0.872519i	$-0.662485\pi$
$19$	−29214.8	−0.977161	−0.488580	+	0.872519i	$0.662485\pi$
$20$	2112.37	0.0590426
$21$	−17592.9	−0.414543
$22$	−53685.1	−1.07492
$23$	65810.5	1.12784	0.563920	−	0.825829i	$-0.309293\pi$
$23$	65810.5	1.12784	0.563920	+	0.825829i	$0.309293\pi$
$24$	13824.0	0.204124
$25$	−77035.6	−0.986056
$26$	31420.7	0.350598
$27$	−19683.0	−0.192450
$28$	41701.7	0.359005
$29$	−30949.5	−0.235646	−0.117823	−	0.993035i	$-0.537592\pi$
$29$	−30949.5	−0.235646	−0.117823	+	0.993035i	$0.537592\pi$
$30$	7129.25	0.0482080
$31$	−201373.	−1.21405	−0.607024	−	0.794684i	$-0.707637\pi$
$31$	−201373.	−1.21405	−0.607024	+	0.794684i	$0.707637\pi$
$32$	−32768.0	−0.176777
$33$	−181187.	−0.877666
$34$	112709.	0.491793
$35$	21506.2	0.0847863
$36$	46656.0	0.166667
$37$	255543.	0.829388	0.414694	−	0.909961i	$-0.363889\pi$
$37$	255543.	0.829388	0.414694	+	0.909961i	$0.363889\pi$
$38$	233719.	0.690957
$39$	106045.	0.286262
$40$	−16899.0	−0.0417494
$41$	−120712.	−0.273532	−0.136766	−	0.990603i	$-0.543671\pi$
$41$	−120712.	−0.273532	−0.136766	+	0.990603i	$0.543671\pi$
$42$	140743.	0.293126
$43$	686859.	1.31743	0.658715	−	0.752392i	$-0.271100\pi$
$43$	686859.	1.31743	0.658715	+	0.752392i	$0.271100\pi$
$44$	429481.	0.760081
$45$	24061.2	0.0393617
$46$	−526484.	−0.797503
$47$	−887083.	−1.24630	−0.623149	−	0.782103i	$-0.714147\pi$
$47$	−887083.	−1.24630	−0.623149	+	0.782103i	$0.714147\pi$
$48$	−110592.	−0.144338
$49$	−398975.	−0.484462
$50$	616285.	0.697247
$51$	380393.	0.401547
$52$	−251366.	−0.247910
$53$	−1.60047e6	−1.47667	−0.738334	−	0.674435i	$-0.764387\pi$
$53$	−1.60047e6	−1.47667	−0.738334	+	0.674435i	$0.764387\pi$
$54$	157464.	0.136083
$55$	221490.	0.179508
$56$	−333613.	−0.253855
$57$	788801.	0.564164
$58$	247596.	0.166627
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−57034.0	−0.0340882
$61$	2.18882e6	1.23469	0.617343	−	0.786694i	$-0.288209\pi$
$61$	2.18882e6	1.23469	0.617343	+	0.786694i	$0.288209\pi$
$62$	1.61098e6	0.858461
$63$	475008.	0.239337
$64$	262144.	0.125000
$65$	−129633.	−0.0585490
$66$	1.44950e6	0.620603
$67$	235145.	0.0955153	0.0477577	−	0.998859i	$-0.484792\pi$
$67$	235145.	0.0955153	0.0477577	+	0.998859i	$0.484792\pi$
$68$	−901671.	−0.347750
$69$	−1.77688e6	−0.651159
$70$	−172050.	−0.0599529
$71$	2.98582e6	0.990056	0.495028	−	0.868877i	$-0.335158\pi$
$71$	2.98582e6	0.990056	0.495028	+	0.868877i	$0.335158\pi$
$72$	−373248.	−0.117851
$73$	−2.63695e6	−0.793363	−0.396682	−	0.917956i	$-0.629838\pi$
$73$	−2.63695e6	−0.793363	−0.396682	+	0.917956i	$0.629838\pi$
$74$	−2.04434e6	−0.586466
$75$	2.07996e6	0.569300
$76$	−1.86975e6	−0.488580
$77$	4.37258e6	1.09149
$78$	−848359.	−0.202418
$79$	6.56186e6	1.49738	0.748691	−	0.662920i	$-0.230683\pi$
$79$	6.56186e6	1.49738	0.748691	+	0.662920i	$0.230683\pi$
$80$	135192.	0.0295213
$81$	531441.	0.111111
$82$	965699.	0.193416
$83$	1.83037e6	0.351371	0.175685	−	0.984446i	$-0.443786\pi$
$83$	1.83037e6	0.351371	0.175685	+	0.984446i	$0.443786\pi$
$84$	−1.12594e6	−0.207272
$85$	−465006.	−0.0821282
$86$	−5.49487e6	−0.931564
$87$	835635.	0.136050
$88$	−3.43585e6	−0.537458
$89$	2.35466e6	0.354049	0.177024	−	0.984206i	$-0.443353\pi$
$89$	2.35466e6	0.354049	0.177024	+	0.984206i	$0.443353\pi$
$90$	−192490.	−0.0278329
$91$	−2.55917e6	−0.356004
$92$	4.21187e6	0.563920
$93$	5.43707e6	0.700930
$94$	7.09666e6	0.881265
$95$	−964259.	−0.115388
$96$	884736.	0.102062
$97$	4.28818e6	0.477059	0.238530	−	0.971135i	$-0.423335\pi$
$97$	4.28818e6	0.477059	0.238530	+	0.971135i	$0.423335\pi$
$98$	3.19180e6	0.342566
$99$	4.89206e6	0.506721
$100$	−4.93028e6	−0.493028
$101$	−1.63660e7	−1.58058	−0.790292	−	0.612730i	$-0.790071\pi$
$101$	−1.63660e7	−1.58058	−0.790292	+	0.612730i	$0.790071\pi$
$102$	−3.04314e6	−0.283937
$103$	1.82357e7	1.64434	0.822170	−	0.569242i	$-0.192763\pi$
$103$	1.82357e7	1.64434	0.822170	+	0.569242i	$0.192763\pi$
$104$	2.01092e6	0.175299
$105$	−580667.	−0.0489514
$106$	1.28038e7	1.04416
$107$	−1.68251e7	−1.32774	−0.663870	−	0.747848i	$-0.731087\pi$
$107$	−1.68251e7	−1.32774	−0.663870	+	0.747848i	$0.731087\pi$
$108$	−1.25971e6	−0.0962250
$109$	−2.10369e7	−1.55592	−0.777962	−	0.628311i	$-0.783747\pi$
$109$	−2.10369e7	−1.55592	−0.777962	+	0.628311i	$0.783747\pi$
$110$	−1.77192e6	−0.126932
$111$	−6.89966e6	−0.478848
$112$	2.66891e6	0.179502
$113$	−8.39028e6	−0.547018	−0.273509	−	0.961869i	$-0.588184\pi$
$113$	−8.39028e6	−0.547018	−0.273509	+	0.961869i	$0.588184\pi$
$114$	−6.31041e6	−0.398924
$115$	2.17213e6	0.133181
$116$	−1.98076e6	−0.117823
$117$	−2.86321e6	−0.165273
$118$	−1.64303e6	−0.0920575
$119$	−9.17998e6	−0.499376
$120$	456272.	0.0241040
$121$	2.55456e7	1.31089
$122$	−1.75106e7	−0.873055
$123$	3.25923e6	0.157924
$124$	−1.28879e7	−0.607024
$125$	−5.12120e6	−0.234524
$126$	−3.80006e6	−0.169236
$127$	9.46335e6	0.409951	0.204976	−	0.978767i	$-0.434289\pi$
$127$	9.46335e6	0.409951	0.204976	+	0.978767i	$0.434289\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.85452e7	−0.760619
$130$	1.03707e6	0.0414004
$131$	2.25177e6	0.0875133	0.0437566	−	0.999042i	$-0.486067\pi$
$131$	2.25177e6	0.0875133	0.0437566	+	0.999042i	$0.486067\pi$
$132$	−1.15960e7	−0.438833
$133$	−1.90361e7	−0.701611
$134$	−1.88116e6	−0.0675395
$135$	−649653.	−0.0227255
$136$	7.21337e6	0.245896
$137$	−1.11965e7	−0.372013	−0.186007	−	0.982548i	$-0.559555\pi$
$137$	−1.11965e7	−0.372013	−0.186007	+	0.982548i	$0.559555\pi$
$138$	1.42151e7	0.460439
$139$	−2.08053e7	−0.657086	−0.328543	−	0.944489i	$-0.606558\pi$
$139$	−2.08053e7	−0.657086	−0.328543	+	0.944489i	$0.606558\pi$
$140$	1.37640e6	0.0423931
$141$	2.39512e7	0.719550
$142$	−2.38866e7	−0.700075
$143$	−2.63566e7	−0.753727
$144$	2.98598e6	0.0833333
$145$	−1.02151e6	−0.0278263
$146$	2.10956e7	0.560993
$147$	1.07723e7	0.279704
$148$	1.63548e7	0.414694
$149$	−2.06109e7	−0.510439	−0.255220	−	0.966883i	$-0.582148\pi$
$149$	−2.06109e7	−0.510439	−0.255220	+	0.966883i	$0.582148\pi$
$150$	−1.66397e7	−0.402556
$151$	4.23533e7	1.00108	0.500539	−	0.865714i	$-0.333135\pi$
$151$	4.23533e7	1.00108	0.500539	+	0.865714i	$0.333135\pi$
$152$	1.49580e7	0.345479
$153$	−1.02706e7	−0.231833
$154$	−3.49806e7	−0.771800
$155$	−6.64648e6	−0.143361
$156$	6.78687e6	0.143131
$157$	−6.18974e7	−1.27651	−0.638254	−	0.769826i	$-0.720343\pi$
$157$	−6.18974e7	−1.27651	−0.638254	+	0.769826i	$0.720343\pi$
$158$	−5.24949e7	−1.05881
$159$	4.32128e7	0.852555
$160$	−1.08153e6	−0.0208747
$161$	4.28813e7	0.809800
$162$	−4.25153e6	−0.0785674
$163$	−5.05770e7	−0.914738	−0.457369	−	0.889277i	$-0.651208\pi$
$163$	−5.05770e7	−0.914738	−0.457369	+	0.889277i	$0.651208\pi$
$164$	−7.72559e6	−0.136766
$165$	−5.98023e6	−0.103639
$166$	−1.46430e7	−0.248457
$167$	−2.24389e7	−0.372816	−0.186408	−	0.982472i	$-0.559685\pi$
$167$	−2.24389e7	−0.372816	−0.186408	+	0.982472i	$0.559685\pi$
$168$	9.00756e6	0.146563
$169$	−4.73226e7	−0.754162
$170$	3.72005e6	0.0580734
$171$	−2.12976e7	−0.325720
$172$	4.39590e7	0.658715
$173$	5.24907e6	0.0770763	0.0385381	−	0.999257i	$-0.487730\pi$
$173$	5.24907e6	0.0770763	0.0385381	+	0.999257i	$0.487730\pi$
$174$	−6.68508e6	−0.0962021
$175$	−5.01955e7	−0.707998
$176$	2.74868e7	0.380040
$177$	−5.54523e6	−0.0751646
$178$	−1.88373e7	−0.250350
$179$	−4.29616e7	−0.559880	−0.279940	−	0.960017i	$-0.590315\pi$
$179$	−4.29616e7	−0.559880	−0.279940	+	0.960017i	$0.590315\pi$
$180$	1.53992e6	0.0196809
$181$	−1.04480e8	−1.30966	−0.654831	−	0.755775i	$-0.727260\pi$
$181$	−1.04480e8	−1.30966	−0.654831	+	0.755775i	$0.727260\pi$
$182$	2.04734e7	0.251733
$183$	−5.90982e7	−0.712846
$184$	−3.36950e7	−0.398752
$185$	8.43440e6	0.0979384
$186$	−4.34966e7	−0.495633
$187$	−9.45437e7	−1.05727
$188$	−5.67733e7	−0.623149
$189$	−1.28252e7	−0.138181
$190$	7.71407e6	0.0815917
$191$	−4.65368e7	−0.483259	−0.241629	−	0.970369i	$-0.577682\pi$
$191$	−4.65368e7	−0.483259	−0.241629	+	0.970369i	$0.577682\pi$
$192$	−7.07789e6	−0.0721688
$193$	−3.19978e7	−0.320383	−0.160192	−	0.987086i	$-0.551211\pi$
$193$	−3.19978e7	−0.320383	−0.160192	+	0.987086i	$0.551211\pi$
$194$	−3.43055e7	−0.337332
$195$	3.50009e6	0.0338033
$196$	−2.55344e7	−0.242231
$197$	−9.71255e7	−0.905111	−0.452555	−	0.891736i	$-0.649488\pi$
$197$	−9.71255e7	−0.905111	−0.452555	+	0.891736i	$0.649488\pi$
$198$	−3.91365e7	−0.358306
$199$	−7.83613e7	−0.704881	−0.352441	−	0.935834i	$-0.614648\pi$
$199$	−7.83613e7	−0.704881	−0.352441	+	0.935834i	$0.614648\pi$
$200$	3.94422e7	0.348623
$201$	−6.34890e6	−0.0551458
$202$	1.30928e8	1.11764
$203$	−2.01663e7	−0.169196
$204$	2.43451e7	0.200774
$205$	−3.98421e6	−0.0323001
$206$	−1.45885e8	−1.16272
$207$	4.79758e7	0.375947
$208$	−1.60874e7	−0.123955
$209$	−1.96050e8	−1.48544
$210$	4.64534e6	0.0346138
$211$	1.39610e8	1.02312	0.511562	−	0.859246i	$-0.329067\pi$
$211$	1.39610e8	1.02312	0.511562	+	0.859246i	$0.329067\pi$
$212$	−1.02430e8	−0.738334
$213$	−8.06172e7	−0.571609
$214$	1.34600e8	0.938854
$215$	2.26703e7	0.155569
$216$	1.00777e7	0.0680414
$217$	−1.31212e8	−0.871698
$218$	1.68295e8	1.10020
$219$	7.11977e7	0.458048
$220$	1.41754e7	0.0897542
$221$	5.53343e7	0.344843
$222$	5.51973e7	0.338596
$223$	2.96843e8	1.79250	0.896250	−	0.443549i	$-0.146281\pi$
$223$	2.96843e8	1.79250	0.896250	+	0.443549i	$0.146281\pi$
$224$	−2.13513e7	−0.126927
$225$	−5.61590e7	−0.328685
$226$	6.71222e7	0.386800
$227$	−1.36250e8	−0.773116	−0.386558	−	0.922265i	$-0.626336\pi$
$227$	−1.36250e8	−0.773116	−0.386558	+	0.922265i	$0.626336\pi$
$228$	5.04833e7	0.282082
$229$	2.08424e8	1.14689	0.573447	−	0.819243i	$-0.305606\pi$
$229$	2.08424e8	1.14689	0.573447	+	0.819243i	$0.305606\pi$
$230$	−1.73770e7	−0.0941733
$231$	−1.18060e8	−0.630172
$232$	1.58461e7	0.0833134
$233$	2.45425e8	1.27108	0.635541	−	0.772067i	$-0.280777\pi$
$233$	2.45425e8	1.27108	0.635541	+	0.772067i	$0.280777\pi$
$234$	2.29057e7	0.116866
$235$	−2.92789e7	−0.147169
$236$	1.31443e7	0.0650945
$237$	−1.77170e8	−0.864513
$238$	7.34398e7	0.353112
$239$	−2.70127e8	−1.27990	−0.639949	−	0.768417i	$-0.721045\pi$
$239$	−2.70127e8	−1.27990	−0.639949	+	0.768417i	$0.721045\pi$
$240$	−3.65018e6	−0.0170441
$241$	−4.02358e8	−1.85163	−0.925813	−	0.377982i	$-0.876618\pi$
$241$	−4.02358e8	−1.85163	−0.925813	+	0.377982i	$0.876618\pi$
$242$	−2.04364e8	−0.926940
$243$	−1.43489e7	−0.0641500
$244$	1.40085e8	0.617343
$245$	−1.31685e7	−0.0572078
$246$	−2.60739e7	−0.111669
$247$	1.14744e8	0.484496
$248$	1.03103e8	0.429230
$249$	−4.94200e7	−0.202864
$250$	4.09696e7	0.165833
$251$	−4.69319e8	−1.87331	−0.936656	−	0.350251i	$-0.886096\pi$
$251$	−4.69319e8	−1.87331	−0.936656	+	0.350251i	$0.886096\pi$
$252$	3.04005e7	0.119668
$253$	4.41631e8	1.71450
$254$	−7.57068e7	−0.289879
$255$	1.25552e7	0.0474167
$256$	1.67772e7	0.0625000
$257$	−1.78819e8	−0.657125	−0.328562	−	0.944482i	$-0.606564\pi$
$257$	−1.78819e8	−0.657125	−0.328562	+	0.944482i	$0.606564\pi$
$258$	1.48361e8	0.537839
$259$	1.66509e8	0.595509
$260$	−8.29652e6	−0.0292745
$261$	−2.25622e7	−0.0785486
$262$	−1.80141e7	−0.0618812
$263$	1.79031e8	0.606851	0.303426	−	0.952855i	$-0.401870\pi$
$263$	1.79031e8	0.606851	0.303426	+	0.952855i	$0.401870\pi$
$264$	9.27679e7	0.310302
$265$	−5.28249e7	−0.174373
$266$	1.52288e8	0.496114
$267$	−6.35758e7	−0.204410
$268$	1.50492e7	0.0477577
$269$	1.75417e8	0.549462	0.274731	−	0.961521i	$-0.411411\pi$
$269$	1.75417e8	0.549462	0.274731	+	0.961521i	$0.411411\pi$
$270$	5.19722e6	0.0160693
$271$	−2.50129e8	−0.763434	−0.381717	−	0.924279i	$-0.624667\pi$
$271$	−2.50129e8	−0.763434	−0.381717	+	0.924279i	$0.624667\pi$
$272$	−5.77070e7	−0.173875
$273$	6.90976e7	0.205539
$274$	8.95716e7	0.263053
$275$	−5.16959e8	−1.49896
$276$	−1.13720e8	−0.325579
$277$	2.32328e8	0.656784	0.328392	−	0.944542i	$-0.393493\pi$
$277$	2.32328e8	0.656784	0.328392	+	0.944542i	$0.393493\pi$
$278$	1.66442e8	0.464630
$279$	−1.46801e8	−0.404682
$280$	−1.10112e7	−0.0299765
$281$	1.08217e8	0.290954	0.145477	−	0.989362i	$-0.453528\pi$
$281$	1.08217e8	0.290954	0.145477	+	0.989362i	$0.453528\pi$
$282$	−1.91610e8	−0.508799
$283$	−5.76165e8	−1.51110	−0.755552	−	0.655088i	$-0.772631\pi$
$283$	−5.76165e8	−1.51110	−0.755552	+	0.655088i	$0.772631\pi$
$284$	1.91093e8	0.495028
$285$	2.60350e7	0.0666194
$286$	2.10853e8	0.532965
$287$	−7.86548e7	−0.196399
$288$	−2.38879e7	−0.0589256
$289$	−2.11850e8	−0.516280
$290$	8.17209e6	0.0196762
$291$	−1.15781e8	−0.275430
$292$	−1.68765e8	−0.396682
$293$	−1.56969e8	−0.364567	−0.182283	−	0.983246i	$-0.558349\pi$
$293$	−1.56969e8	−0.364567	−0.182283	+	0.983246i	$0.558349\pi$
$294$	−8.61787e7	−0.197781
$295$	6.77870e6	0.0153734
$296$	−1.30838e8	−0.293233
$297$	−1.32086e8	−0.292555
$298$	1.64887e8	0.360935
$299$	−2.58476e8	−0.559206
$300$	1.33118e8	0.284650
$301$	4.47549e8	0.945928
$302$	−3.38826e8	−0.707869
$303$	4.41882e8	0.912551
$304$	−1.19664e8	−0.244290
$305$	7.22439e7	0.145798
$306$	8.21648e7	0.163931
$307$	3.67539e8	0.724969	0.362485	−	0.931990i	$-0.381929\pi$
$307$	3.67539e8	0.724969	0.362485	+	0.931990i	$0.381929\pi$
$308$	2.79845e8	0.545745
$309$	−4.92363e8	−0.949360
$310$	5.31718e7	0.101371
$311$	−5.87757e8	−1.10799	−0.553996	−	0.832520i	$-0.686898\pi$
$311$	−5.87757e8	−1.10799	−0.553996	+	0.832520i	$0.686898\pi$
$312$	−5.42950e7	−0.101209
$313$	5.70073e8	1.05081	0.525406	−	0.850851i	$-0.323913\pi$
$313$	5.70073e8	1.05081	0.525406	+	0.850851i	$0.323913\pi$
$314$	4.95179e8	0.902628
$315$	1.56780e7	0.0282621
$316$	4.19959e8	0.748691
$317$	5.27215e8	0.929566	0.464783	−	0.885425i	$-0.346132\pi$
$317$	5.27215e8	0.929566	0.464783	+	0.885425i	$0.346132\pi$
$318$	−3.45702e8	−0.602847
$319$	−2.07691e8	−0.358220
$320$	8.65227e6	0.0147606
$321$	4.54277e8	0.766571
$322$	−3.43051e8	−0.572615
$323$	4.11597e8	0.679615
$324$	3.40122e7	0.0555556
$325$	3.02564e8	0.488906
$326$	4.04616e8	0.646817
$327$	5.67996e8	0.898313
$328$	6.18047e7	0.0967082
$329$	−5.78013e8	−0.894854
$330$	4.78419e7	0.0732840
$331$	2.51163e8	0.380679	0.190339	−	0.981718i	$-0.439041\pi$
$331$	2.51163e8	0.380679	0.190339	+	0.981718i	$0.439041\pi$
$332$	1.17144e8	0.175685
$333$	1.86291e8	0.276463
$334$	1.79511e8	0.263621
$335$	7.76113e6	0.0112789
$336$	−7.20605e7	−0.103636
$337$	−8.63320e8	−1.22876	−0.614380	−	0.789010i	$-0.710594\pi$
$337$	−8.63320e8	−1.22876	−0.614380	+	0.789010i	$0.710594\pi$
$338$	3.78581e8	0.533273
$339$	2.26538e8	0.315821
$340$	−2.97604e7	−0.0410641
$341$	−1.35134e9	−1.84555
$342$	1.70381e8	0.230319
$343$	−7.96579e8	−1.06586
$344$	−3.51672e8	−0.465782
$345$	−5.86474e7	−0.0768922
$346$	−4.19925e7	−0.0545012
$347$	8.11645e8	1.04283	0.521414	−	0.853304i	$-0.325405\pi$
$347$	8.11645e8	1.04283	0.521414	+	0.853304i	$0.325405\pi$
$348$	5.34807e7	0.0680251
$349$	1.34700e9	1.69620	0.848102	−	0.529833i	$-0.177745\pi$
$349$	1.34700e9	1.69620	0.848102	+	0.529833i	$0.177745\pi$
$350$	4.01564e8	0.500630
$351$	7.73067e7	0.0954206
$352$	−2.19894e8	−0.268729
$353$	1.07254e9	1.29778	0.648892	−	0.760881i	$-0.275233\pi$
$353$	1.07254e9	1.29778	0.648892	+	0.760881i	$0.275233\pi$
$354$	4.43619e7	0.0531494
$355$	9.85495e7	0.116911
$356$	1.50698e8	0.177024
$357$	2.47859e8	0.288315
$358$	3.43693e8	0.395895
$359$	−1.44710e9	−1.65070	−0.825352	−	0.564618i	$-0.809023\pi$
$359$	−1.44710e9	−1.65070	−0.825352	+	0.564618i	$0.809023\pi$
$360$	−1.23193e7	−0.0139165
$361$	−4.03644e7	−0.0451568
$362$	8.35842e8	0.926071
$363$	−6.89730e8	−0.756843
$364$	−1.63787e8	−0.178002
$365$	−8.70347e7	−0.0936844
$366$	4.72786e8	0.504058
$367$	1.80575e8	0.190689	0.0953446	−	0.995444i	$-0.469605\pi$
$367$	1.80575e8	0.190689	0.0953446	+	0.995444i	$0.469605\pi$
$368$	2.69560e8	0.281960
$369$	−8.79993e7	−0.0911774
$370$	−6.74752e7	−0.0692529
$371$	−1.04285e9	−1.06026
$372$	3.47973e8	0.350465
$373$	5.61788e8	0.560521	0.280261	−	0.959924i	$-0.409579\pi$
$373$	5.61788e8	0.560521	0.280261	+	0.959924i	$0.409579\pi$
$374$	7.56349e8	0.747604
$375$	1.38272e8	0.135402
$376$	4.54186e8	0.440633
$377$	1.21557e8	0.116838
$378$	1.02602e8	0.0977087
$379$	1.23275e9	1.16315	0.581577	−	0.813492i	$-0.302436\pi$
$379$	1.23275e9	1.16315	0.581577	+	0.813492i	$0.302436\pi$
$380$	−6.17126e7	−0.0576941
$381$	−2.55511e8	−0.236685
$382$	3.72295e8	0.341716
$383$	−1.07845e9	−0.980855	−0.490428	−	0.871482i	$-0.663159\pi$
$383$	−1.07845e9	−0.980855	−0.490428	+	0.871482i	$0.663159\pi$
$384$	5.66231e7	0.0510310
$385$	1.44320e8	0.128889
$386$	2.55982e8	0.226545
$387$	5.00720e8	0.439144
$388$	2.74444e8	0.238530
$389$	4.19555e8	0.361381	0.180691	−	0.983540i	$-0.442167\pi$
$389$	4.19555e8	0.361381	0.180691	+	0.983540i	$0.442167\pi$
$390$	−2.80008e7	−0.0239025
$391$	−9.27178e8	−0.784413
$392$	2.04275e8	0.171283
$393$	−6.07977e7	−0.0505258
$394$	7.77004e8	0.640010
$395$	2.16580e8	0.176818
$396$	3.13092e8	0.253360
$397$	−1.12725e9	−0.904174	−0.452087	−	0.891974i	$-0.649320\pi$
$397$	−1.12725e9	−0.904174	−0.452087	+	0.891974i	$0.649320\pi$
$398$	6.26891e8	0.498426
$399$	5.13974e8	0.405075
$400$	−3.15538e8	−0.246514
$401$	−7.97243e8	−0.617427	−0.308713	−	0.951155i	$-0.599898\pi$
$401$	−7.97243e8	−0.617427	−0.308713	+	0.951155i	$0.599898\pi$
$402$	5.07912e7	0.0389940
$403$	7.90910e8	0.601949
$404$	−1.04742e9	−0.790292
$405$	1.75406e7	0.0131206
$406$	1.61330e8	0.119640
$407$	1.71486e9	1.26080
$408$	−1.94761e8	−0.141968
$409$	1.26001e9	0.910629	0.455314	−	0.890331i	$-0.349527\pi$
$409$	1.26001e9	0.910629	0.455314	+	0.890331i	$0.349527\pi$
$410$	3.18737e7	0.0228396
$411$	3.02304e8	0.214782
$412$	1.16708e9	0.822170
$413$	1.33823e8	0.0934769
$414$	−3.83807e8	−0.265834
$415$	6.04129e7	0.0414917
$416$	1.28699e8	0.0876494
$417$	5.61743e8	0.379369
$418$	1.56840e9	1.05037
$419$	2.50914e9	1.66639	0.833193	−	0.552983i	$-0.186510\pi$
$419$	2.50914e9	1.66639	0.833193	+	0.552983i	$0.186510\pi$
$420$	−3.71627e7	−0.0244757
$421$	7.48023e8	0.488571	0.244285	−	0.969703i	$-0.421447\pi$
$421$	7.48023e8	0.488571	0.244285	+	0.969703i	$0.421447\pi$
$422$	−1.11688e9	−0.723458
$423$	−6.46683e8	−0.415432
$424$	8.19442e8	0.522081
$425$	1.08533e9	0.685802
$426$	6.44938e8	0.404189
$427$	1.42621e9	0.886516
$428$	−1.07680e9	−0.663870
$429$	7.11629e8	0.435164
$430$	−1.81363e8	−0.110004
$431$	2.85439e8	0.171729	0.0858645	−	0.996307i	$-0.472635\pi$
$431$	2.85439e8	0.171729	0.0858645	+	0.996307i	$0.472635\pi$
$432$	−8.06216e7	−0.0481125
$433$	7.15829e8	0.423742	0.211871	−	0.977298i	$-0.432044\pi$
$433$	7.15829e8	0.423742	0.211871	+	0.977298i	$0.432044\pi$
$434$	1.04970e9	0.616383
$435$	2.75808e7	0.0160655
$436$	−1.34636e9	−0.777962
$437$	−1.92264e9	−1.10208
$438$	−5.69581e8	−0.323889
$439$	−1.24735e9	−0.703661	−0.351830	−	0.936064i	$-0.614441\pi$
$439$	−1.24735e9	−0.703661	−0.351830	+	0.936064i	$0.614441\pi$
$440$	−1.13403e8	−0.0634658
$441$	−2.90853e8	−0.161487
$442$	−4.42674e8	−0.243841
$443$	3.33501e8	0.182257	0.0911284	−	0.995839i	$-0.470953\pi$
$443$	3.33501e8	0.182257	0.0911284	+	0.995839i	$0.470953\pi$
$444$	−4.41578e8	−0.239424
$445$	7.77174e7	0.0418079
$446$	−2.37474e9	−1.26749
$447$	5.56493e8	0.294702
$448$	1.70810e8	0.0897512
$449$	−2.71541e9	−1.41571	−0.707854	−	0.706359i	$-0.750336\pi$
$449$	−2.71541e9	−1.41571	−0.707854	+	0.706359i	$0.750336\pi$
$450$	4.49272e8	0.232416
$451$	−8.10058e8	−0.415813
$452$	−5.36978e8	−0.273509
$453$	−1.14354e9	−0.577972
$454$	1.09000e9	0.546676
$455$	−8.44675e7	−0.0420387
$456$	−4.03866e8	−0.199462
$457$	1.69767e8	0.0832046	0.0416023	−	0.999134i	$-0.486754\pi$
$457$	1.69767e8	0.0832046	0.0416023	+	0.999134i	$0.486754\pi$
$458$	−1.66739e9	−0.810977
$459$	2.77306e8	0.133849
$460$	1.39016e8	0.0665906
$461$	−1.71105e9	−0.813410	−0.406705	−	0.913560i	$-0.633322\pi$
$461$	−1.71105e9	−0.813410	−0.406705	+	0.913560i	$0.633322\pi$
$462$	9.44477e8	0.445599
$463$	3.52144e9	1.64887	0.824436	−	0.565955i	$-0.191493\pi$
$463$	3.52144e9	1.64887	0.824436	+	0.565955i	$0.191493\pi$
$464$	−1.26769e8	−0.0589115
$465$	1.79455e8	0.0827695
$466$	−1.96340e9	−0.898791
$467$	−3.57424e9	−1.62396	−0.811978	−	0.583688i	$-0.801609\pi$
$467$	−3.57424e9	−1.62396	−0.811978	+	0.583688i	$0.801609\pi$
$468$	−1.83246e8	−0.0826367
$469$	1.53217e8	0.0685809
$470$	2.34231e8	0.104064
$471$	1.67123e9	0.736992
$472$	−1.05154e8	−0.0460287
$473$	4.60926e9	2.00271
$474$	1.41736e9	0.611303
$475$	2.25058e9	0.963535
$476$	−5.87519e8	−0.249688
$477$	−1.16675e9	−0.492223
$478$	2.16102e9	0.905025
$479$	−1.65581e9	−0.688391	−0.344196	−	0.938898i	$-0.611848\pi$
$479$	−1.65581e9	−0.688391	−0.344196	+	0.938898i	$0.611848\pi$
$480$	2.92014e7	0.0120520
$481$	−1.00367e9	−0.411227
$482$	3.21887e9	1.30930
$483$	−1.15780e9	−0.467538
$484$	1.63492e9	0.655446
$485$	1.41535e8	0.0563336
$486$	1.14791e8	0.0453609
$487$	−2.77776e9	−1.08979	−0.544895	−	0.838504i	$-0.683431\pi$
$487$	−2.77776e9	−1.08979	−0.544895	+	0.838504i	$0.683431\pi$
$488$	−1.12068e9	−0.436527
$489$	1.36558e9	0.528124
$490$	1.05348e8	0.0404520
$491$	−4.57724e9	−1.74509	−0.872546	−	0.488532i	$-0.837533\pi$
$491$	−4.57724e9	−1.74509	−0.872546	+	0.488532i	$0.837533\pi$
$492$	2.08591e8	0.0789619
$493$	4.36035e8	0.163892
$494$	−9.17951e8	−0.342590
$495$	1.61466e8	0.0598362
$496$	−8.24824e8	−0.303512
$497$	1.94553e9	0.710870
$498$	3.95360e8	0.143447
$499$	−1.87823e9	−0.676701	−0.338351	−	0.941020i	$-0.609869\pi$
$499$	−1.87823e9	−0.676701	−0.338351	+	0.941020i	$0.609869\pi$
$500$	−3.27757e8	−0.117262
$501$	6.05851e8	0.215245
$502$	3.75455e9	1.32463
$503$	−4.72831e9	−1.65660	−0.828300	−	0.560284i	$-0.810692\pi$
$503$	−4.72831e9	−1.65660	−0.828300	+	0.560284i	$0.810692\pi$
$504$	−2.43204e8	−0.0846182
$505$	−5.40173e8	−0.186644
$506$	−3.53304e9	−1.21233
$507$	1.27771e9	0.435416
$508$	6.05655e8	0.204976
$509$	4.14667e8	0.139376	0.0696880	−	0.997569i	$-0.477800\pi$
$509$	4.14667e8	0.139376	0.0696880	+	0.997569i	$0.477800\pi$
$510$	−1.00441e8	−0.0335287
$511$	−1.71821e9	−0.569642
$512$	−1.34218e8	−0.0441942
$513$	5.75036e8	0.188055
$514$	1.43055e9	0.464657
$515$	6.01883e8	0.194172
$516$	−1.18689e9	−0.380310
$517$	−5.95290e9	−1.89457
$518$	−1.33207e9	−0.421088
$519$	−1.41725e8	−0.0445000
$520$	6.63722e7	0.0207002
$521$	1.04334e9	0.323216	0.161608	−	0.986855i	$-0.448332\pi$
$521$	1.04334e9	0.323216	0.161608	+	0.986855i	$0.448332\pi$
$522$	1.80497e8	0.0555423
$523$	−5.19714e9	−1.58858	−0.794289	−	0.607541i	$-0.792156\pi$
$523$	−5.19714e9	−1.58858	−0.794289	+	0.607541i	$0.792156\pi$
$524$	1.44113e8	0.0437566
$525$	1.35528e9	0.408763
$526$	−1.43225e9	−0.429109
$527$	2.83707e9	0.844370
$528$	−7.42143e8	−0.219416
$529$	9.26193e8	0.272024
$530$	4.22599e8	0.123300
$531$	1.49721e8	0.0433963
$532$	−1.21831e9	−0.350805
$533$	4.74108e8	0.135623
$534$	5.08606e8	0.144540
$535$	−5.55324e8	−0.156786
$536$	−1.20394e8	−0.0337698
$537$	1.15996e9	0.323247
$538$	−1.40333e9	−0.388528
$539$	−2.67738e9	−0.736461
$540$	−4.15778e7	−0.0113627
$541$	−1.93308e9	−0.524879	−0.262439	−	0.964948i	$-0.584527\pi$
$541$	−1.93308e9	−0.524879	−0.262439	+	0.964948i	$0.584527\pi$
$542$	2.00103e9	0.539829
$543$	2.82097e9	0.756134
$544$	4.61656e8	0.122948
$545$	−6.94339e8	−0.183732
$546$	−5.52781e8	−0.145338
$547$	3.97590e9	1.03868	0.519338	−	0.854569i	$-0.326179\pi$
$547$	3.97590e9	1.03868	0.519338	+	0.854569i	$0.326179\pi$
$548$	−7.16573e8	−0.186007
$549$	1.59565e9	0.411562
$550$	4.13567e9	1.05993
$551$	9.04184e8	0.230264
$552$	9.09764e8	0.230219
$553$	4.27564e9	1.07513
$554$	−1.85862e9	−0.464416
$555$	−2.27729e8	−0.0565448
$556$	−1.33154e9	−0.328543
$557$	−6.22705e9	−1.52682	−0.763412	−	0.645912i	$-0.776477\pi$
$557$	−6.22705e9	−1.52682	−0.763412	+	0.645912i	$0.776477\pi$
$558$	1.17441e9	0.286154
$559$	−2.69770e9	−0.653209
$560$	8.80894e7	0.0211966
$561$	2.55268e9	0.610416
$562$	−8.65739e8	−0.205736
$563$	−6.99550e9	−1.65211	−0.826055	−	0.563589i	$-0.809420\pi$
$563$	−6.99550e9	−1.65211	−0.826055	+	0.563589i	$0.809420\pi$
$564$	1.53288e9	0.359775
$565$	−2.76928e8	−0.0645947
$566$	4.60932e9	1.06851
$567$	3.46281e8	0.0797788
$568$	−1.52874e9	−0.350038
$569$	−2.56009e9	−0.582589	−0.291295	−	0.956633i	$-0.594086\pi$
$569$	−2.56009e9	−0.582589	−0.291295	+	0.956633i	$0.594086\pi$
$570$	−2.08280e8	−0.0471070
$571$	−2.66754e9	−0.599632	−0.299816	−	0.953997i	$-0.596925\pi$
$571$	−2.66754e9	−0.599632	−0.299816	+	0.953997i	$0.596925\pi$
$572$	−1.68682e9	−0.376863
$573$	1.25649e9	0.279010
$574$	6.29238e8	0.138875
$575$	−5.06975e9	−1.11211
$576$	1.91103e8	0.0416667
$577$	4.02963e9	0.873272	0.436636	−	0.899638i	$-0.356170\pi$
$577$	4.02963e9	0.873272	0.436636	+	0.899638i	$0.356170\pi$
$578$	1.69480e9	0.365065
$579$	8.63940e8	0.184973
$580$	−6.53767e7	−0.0139131
$581$	1.19265e9	0.252288
$582$	9.26248e8	0.194759
$583$	−1.07402e10	−2.24477
$584$	1.35012e9	0.280496
$585$	−9.45026e7	−0.0195163
$586$	1.25575e9	0.257788
$587$	1.27457e9	0.260094	0.130047	−	0.991508i	$-0.458487\pi$
$587$	1.27457e9	0.260094	0.130047	+	0.991508i	$0.458487\pi$
$588$	6.89430e8	0.139852
$589$	5.88308e9	1.18632
$590$	−5.42296e7	−0.0108706
$591$	2.62239e9	0.522566
$592$	1.04670e9	0.207347
$593$	1.04654e6	0.000206094 0	0.000103047	−	1.00000i	$-0.499967\pi$
$593$	1.04654e6	0.000206094 0	0.000103047		1.00000i	$0.499967\pi$
$594$	1.05668e9	0.206868
$595$	−3.02992e8	−0.0589688
$596$	−1.31909e9	−0.255220
$597$	2.11576e9	0.406963
$598$	2.06781e9	0.395418
$599$	−5.04975e9	−0.960010	−0.480005	−	0.877266i	$-0.659365\pi$
$599$	−5.04975e9	−0.960010	−0.480005	+	0.877266i	$0.659365\pi$
$600$	−1.06494e9	−0.201278
$601$	−8.67452e9	−1.62999	−0.814994	−	0.579469i	$-0.803260\pi$
$601$	−8.67452e9	−1.62999	−0.814994	+	0.579469i	$0.803260\pi$
$602$	−3.58039e9	−0.668872
$603$	1.71420e8	0.0318384
$604$	2.71061e9	0.500539
$605$	8.43152e8	0.154797
$606$	−3.53506e9	−0.645271
$607$	6.54478e9	1.18778	0.593888	−	0.804548i	$-0.297592\pi$
$607$	6.54478e9	1.18778	0.593888	+	0.804548i	$0.297592\pi$
$608$	9.57312e8	0.172739
$609$	5.44490e8	0.0976854
$610$	−5.77951e8	−0.103095
$611$	3.48410e9	0.617939
$612$	−6.57318e8	−0.115917
$613$	3.66122e8	0.0641968	0.0320984	−	0.999485i	$-0.489781\pi$
$613$	3.66122e8	0.0641968	0.0320984	+	0.999485i	$0.489781\pi$
$614$	−2.94031e9	−0.512631
$615$	1.07574e8	0.0186485
$616$	−2.23876e9	−0.385900
$617$	−4.26342e9	−0.730735	−0.365367	−	0.930863i	$-0.619057\pi$
$617$	−4.26342e9	−0.730735	−0.365367	+	0.930863i	$0.619057\pi$
$618$	3.93891e9	0.671299
$619$	−8.88413e9	−1.50556	−0.752779	−	0.658273i	$-0.771287\pi$
$619$	−8.88413e9	−1.50556	−0.752779	+	0.658273i	$0.771287\pi$
$620$	−4.25375e8	−0.0716805
$621$	−1.29535e9	−0.217053
$622$	4.70206e9	0.783468
$623$	1.53427e9	0.254210
$624$	4.34360e8	0.0715655
$625$	5.84938e9	0.958362
$626$	−4.56058e9	−0.743037
$627$	5.29336e9	0.857620
$628$	−3.96143e9	−0.638254
$629$	−3.60025e9	−0.576840
$630$	−1.25424e8	−0.0199843
$631$	−7.62749e9	−1.20859	−0.604295	−	0.796761i	$-0.706545\pi$
$631$	−7.62749e9	−1.20859	−0.604295	+	0.796761i	$0.706545\pi$
$632$	−3.35967e9	−0.529404
$633$	−3.76948e9	−0.590701
$634$	−4.21772e9	−0.657302
$635$	3.12346e8	0.0484091
$636$	2.76562e9	0.426277
$637$	1.56701e9	0.240206
$638$	1.66153e9	0.253300
$639$	2.17666e9	0.330019
$640$	−6.92182e7	−0.0104373
$641$	1.06493e9	0.159704	0.0798522	−	0.996807i	$-0.474555\pi$
$641$	1.06493e9	0.159704	0.0798522	+	0.996807i	$0.474555\pi$
$642$	−3.63421e9	−0.542048
$643$	4.45616e8	0.0661031	0.0330516	−	0.999454i	$-0.489477\pi$
$643$	4.45616e8	0.0661031	0.0330516	+	0.999454i	$0.489477\pi$
$644$	2.74441e9	0.404900
$645$	−6.12099e8	−0.0898178
$646$	−3.29277e9	−0.480560
$647$	3.71030e9	0.538573	0.269286	−	0.963060i	$-0.413212\pi$
$647$	3.71030e9	0.538573	0.269286	+	0.963060i	$0.413212\pi$
$648$	−2.72098e8	−0.0392837
$649$	1.37823e9	0.197908
$650$	−2.42051e9	−0.345709
$651$	3.54274e9	0.503275
$652$	−3.23693e9	−0.457369
$653$	−3.91527e9	−0.550257	−0.275128	−	0.961407i	$-0.588720\pi$
$653$	−3.91527e9	−0.550257	−0.275128	+	0.961407i	$0.588720\pi$
$654$	−4.54397e9	−0.635203
$655$	7.43213e7	0.0103340
$656$	−4.94438e8	−0.0683830
$657$	−1.92234e9	−0.264454
$658$	4.62410e9	0.632757
$659$	3.35091e9	0.456104	0.228052	−	0.973649i	$-0.426764\pi$
$659$	3.35091e9	0.456104	0.228052	+	0.973649i	$0.426764\pi$
$660$	−3.82735e8	−0.0518196
$661$	−1.64746e9	−0.221876	−0.110938	−	0.993827i	$-0.535386\pi$
$661$	−1.64746e9	−0.221876	−0.110938	+	0.993827i	$0.535386\pi$
$662$	−2.00931e9	−0.269180
$663$	−1.49402e9	−0.199095
$664$	−9.37150e8	−0.124228
$665$	−6.28300e8	−0.0828498
$666$	−1.49033e9	−0.195489
$667$	−2.03680e9	−0.265771
$668$	−1.43609e9	−0.186408
$669$	−8.01475e9	−1.03490
$670$	−6.20891e7	−0.00797541
$671$	1.46884e10	1.87692
$672$	5.76484e8	0.0732816
$673$	1.37108e10	1.73385	0.866923	−	0.498442i	$-0.166094\pi$
$673$	1.37108e10	1.73385	0.866923	+	0.498442i	$0.166094\pi$
$674$	6.90656e9	0.868864
$675$	1.51629e9	0.189767
$676$	−3.02864e9	−0.377081
$677$	3.87549e8	0.0480028	0.0240014	−	0.999712i	$-0.492359\pi$
$677$	3.87549e8	0.0480028	0.0240014	+	0.999712i	$0.492359\pi$
$678$	−1.81230e9	−0.223319
$679$	2.79413e9	0.342533
$680$	2.38083e8	0.0290367
$681$	3.67874e9	0.446359
$682$	1.08107e10	1.30500
$683$	1.15123e10	1.38258	0.691288	−	0.722580i	$-0.257044\pi$
$683$	1.15123e10	1.38258	0.691288	+	0.722580i	$0.257044\pi$
$684$	−1.36305e9	−0.162860
$685$	−3.69548e8	−0.0439292
$686$	6.37263e9	0.753676
$687$	−5.62745e9	−0.662160
$688$	2.81337e9	0.329358
$689$	6.28600e9	0.732162
$690$	4.69179e8	0.0543710
$691$	2.06205e9	0.237753	0.118877	−	0.992909i	$-0.462071\pi$
$691$	2.06205e9	0.237753	0.118877	+	0.992909i	$0.462071\pi$
$692$	3.35940e8	0.0385381
$693$	3.18761e9	0.363830
$694$	−6.49316e9	−0.737391
$695$	−6.86695e8	−0.0775921
$696$	−4.27845e8	−0.0481010
$697$	1.70067e9	0.190242
$698$	−1.07760e10	−1.19940
$699$	−6.62649e9	−0.733860
$700$	−3.21251e9	−0.353999
$701$	9.41170e9	1.03194	0.515971	−	0.856606i	$-0.327431\pi$
$701$	9.41170e9	1.03194	0.515971	+	0.856606i	$0.327431\pi$
$702$	−6.18454e8	−0.0674726
$703$	−7.46565e9	−0.810446
$704$	1.75915e9	0.190020
$705$	7.90530e8	0.0849682
$706$	−8.58032e9	−0.917671
$707$	−1.06639e10	−1.13487
$708$	−3.54895e8	−0.0375823
$709$	1.30542e10	1.37559	0.687795	−	0.725905i	$-0.258579\pi$
$709$	1.30542e10	1.37559	0.687795	+	0.725905i	$0.258579\pi$
$710$	−7.88396e8	−0.0826685
$711$	4.78360e9	0.499127
$712$	−1.20559e9	−0.125175
$713$	−1.32525e10	−1.36925
$714$	−1.98288e9	−0.203869
$715$	−8.69922e8	−0.0890039
$716$	−2.74954e9	−0.279940
$717$	7.29343e9	0.738950
$718$	1.15768e10	1.16722
$719$	−7.05433e9	−0.707790	−0.353895	−	0.935285i	$-0.615143\pi$
$719$	−7.05433e9	−0.707790	−0.353895	+	0.935285i	$0.615143\pi$
$720$	9.85548e7	0.00984043
$721$	1.18822e10	1.18065
$722$	3.22915e8	0.0319307
$723$	1.08637e10	1.06904
$724$	−6.68674e9	−0.654831
$725$	2.38421e9	0.232360
$726$	5.51784e9	0.535169
$727$	−1.48272e10	−1.43116	−0.715580	−	0.698531i	$-0.753837\pi$
$727$	−1.48272e10	−1.43116	−0.715580	+	0.698531i	$0.753837\pi$
$728$	1.31030e9	0.125866
$729$	3.87420e8	0.0370370
$730$	6.96277e8	0.0662449
$731$	−9.67689e9	−0.916273
$732$	−3.78229e9	−0.356423
$733$	−1.45654e10	−1.36603	−0.683013	−	0.730407i	$-0.739331\pi$
$733$	−1.45654e10	−1.36603	−0.683013	+	0.730407i	$0.739331\pi$
$734$	−1.44460e9	−0.134838
$735$	3.55550e8	0.0330289
$736$	−2.15648e9	−0.199376
$737$	1.57797e9	0.145199
$738$	7.03995e8	0.0644721
$739$	1.19912e10	1.09297	0.546483	−	0.837470i	$-0.315966\pi$
$739$	1.19912e10	1.09297	0.546483	+	0.837470i	$0.315966\pi$
$740$	5.39802e8	0.0489692
$741$	−3.09808e9	−0.279724
$742$	8.34280e9	0.749718
$743$	−3.89599e9	−0.348463	−0.174231	−	0.984705i	$-0.555744\pi$
$743$	−3.89599e9	−0.348463	−0.174231	+	0.984705i	$0.555744\pi$
$744$	−2.78378e9	−0.247816
$745$	−6.80278e8	−0.0602753
$746$	−4.49431e9	−0.396348
$747$	1.33434e9	0.117124
$748$	−6.05079e9	−0.528636
$749$	−1.09630e10	−0.953331
$750$	−1.10618e9	−0.0957439
$751$	5.65844e9	0.487480	0.243740	−	0.969841i	$-0.421626\pi$
$751$	5.65844e9	0.487480	0.243740	+	0.969841i	$0.421626\pi$
$752$	−3.63349e9	−0.311574
$753$	1.26716e10	1.08156
$754$	−9.72453e8	−0.0826169
$755$	1.39790e9	0.118212
$756$	−8.20814e8	−0.0690905
$757$	−2.08902e10	−1.75028	−0.875138	−	0.483874i	$-0.839229\pi$
$757$	−2.08902e10	−1.75028	−0.875138	+	0.483874i	$0.839229\pi$
$758$	−9.86198e9	−0.822474
$759$	−1.19240e10	−0.989867
$760$	4.93701e8	0.0407959
$761$	−7.92618e9	−0.651955	−0.325978	−	0.945377i	$-0.605693\pi$
$761$	−7.92618e9	−0.651955	−0.325978	+	0.945377i	$0.605693\pi$
$762$	2.04408e9	0.167362
$763$	−1.37074e10	−1.11717
$764$	−2.97836e9	−0.241629
$765$	−3.38989e8	−0.0273761
$766$	8.62761e9	0.693569
$767$	−8.06644e8	−0.0645503
$768$	−4.52985e8	−0.0360844
$769$	−1.98497e10	−1.57402	−0.787012	−	0.616938i	$-0.788373\pi$
$769$	−1.98497e10	−1.57402	−0.787012	+	0.616938i	$0.788373\pi$
$770$	−1.15456e9	−0.0911381
$771$	4.82811e9	0.379391
$772$	−2.04786e9	−0.160192
$773$	7.22332e9	0.562482	0.281241	−	0.959637i	$-0.409254\pi$
$773$	7.22332e9	0.562482	0.281241	+	0.959637i	$0.409254\pi$
$774$	−4.00576e9	−0.310521
$775$	1.55129e10	1.19712
$776$	−2.19555e9	−0.168666
$777$	−4.49574e9	−0.343817
$778$	−3.35644e9	−0.255535
$779$	3.52659e9	0.267285
$780$	2.24006e8	0.0169016
$781$	2.00368e10	1.50505
$782$	7.41743e9	0.554664
$783$	6.09178e8	0.0453501
$784$	−1.63420e9	−0.121116
$785$	−2.04297e9	−0.150737
$786$	4.86382e8	0.0357271
$787$	9.59199e8	0.0701451	0.0350726	−	0.999385i	$-0.488834\pi$
$787$	9.59199e8	0.0701451	0.0350726	+	0.999385i	$0.488834\pi$
$788$	−6.21604e9	−0.452555
$789$	−4.83383e9	−0.350366
$790$	−1.73264e9	−0.125030
$791$	−5.46701e9	−0.392764
$792$	−2.50473e9	−0.179153
$793$	−8.59680e9	−0.612182
$794$	9.01797e9	0.639347
$795$	1.42627e9	0.100674
$796$	−5.01512e9	−0.352441
$797$	−5.03548e9	−0.352320	−0.176160	−	0.984362i	$-0.556368\pi$
$797$	−5.03548e9	−0.352320	−0.176160	+	0.984362i	$0.556368\pi$
$798$	−4.11179e9	−0.286431
$799$	1.24978e10	0.866800
$800$	2.52430e9	0.174312
$801$	1.71655e9	0.118016
$802$	6.37794e9	0.436587
$803$	−1.76956e10	−1.20604
$804$	−4.06330e8	−0.0275729
$805$	1.41533e9	0.0956254
$806$	−6.32728e9	−0.425642
$807$	−4.73625e9	−0.317232
$808$	8.37939e9	0.558821
$809$	2.14459e10	1.42405	0.712023	−	0.702157i	$-0.247779\pi$
$809$	2.14459e10	1.42405	0.712023	+	0.702157i	$0.247779\pi$
$810$	−1.40325e8	−0.00927764
$811$	2.75482e8	0.0181351	0.00906754	−	0.999959i	$-0.497114\pi$
$811$	2.75482e8	0.0181351	0.00906754	+	0.999959i	$0.497114\pi$
$812$	−1.29064e9	−0.0845980
$813$	6.75348e9	0.440769
$814$	−1.37189e10	−0.891523
$815$	−1.66934e9	−0.108017
$816$	1.55809e9	0.100387
$817$	−2.00665e10	−1.28734
$818$	−1.00801e10	−0.643912
$819$	−1.86564e9	−0.118668
$820$	−2.54989e8	−0.0161500
$821$	−9.10050e9	−0.573937	−0.286968	−	0.957940i	$-0.592647\pi$
$821$	−9.10050e9	−0.573937	−0.286968	+	0.957940i	$0.592647\pi$
$822$	−2.41843e9	−0.151874
$823$	−1.21109e9	−0.0757316	−0.0378658	−	0.999283i	$-0.512056\pi$
$823$	−1.21109e9	−0.0757316	−0.0378658	+	0.999283i	$0.512056\pi$
$824$	−9.33667e9	−0.581362
$825$	1.39579e10	0.865427
$826$	−1.07058e9	−0.0660981
$827$	2.96671e10	1.82392	0.911961	−	0.410277i	$-0.134568\pi$
$827$	2.96671e10	1.82392	0.911961	+	0.410277i	$0.134568\pi$
$828$	3.07045e9	0.187973
$829$	−9.20544e9	−0.561182	−0.280591	−	0.959827i	$-0.590530\pi$
$829$	−9.20544e9	−0.561182	−0.280591	+	0.959827i	$0.590530\pi$
$830$	−4.83303e8	−0.0293390
$831$	−6.27286e9	−0.379194
$832$	−1.02959e9	−0.0619775
$833$	5.62101e9	0.336943
$834$	−4.49394e9	−0.268254
$835$	−7.40615e8	−0.0440240
$836$	−1.25472e10	−0.742721
$837$	3.96363e9	0.233643
$838$	−2.00731e10	−1.17831
$839$	1.49748e9	0.0875378	0.0437689	−	0.999042i	$-0.486063\pi$
$839$	1.49748e9	0.0875378	0.0437689	+	0.999042i	$0.486063\pi$
$840$	2.97302e8	0.0173069
$841$	−1.62920e10	−0.944471
$842$	−5.98418e9	−0.345472
$843$	−2.92187e9	−0.167983
$844$	8.93505e9	0.511562
$845$	−1.56192e9	−0.0890554
$846$	5.17347e9	0.293755
$847$	1.66452e10	0.941232
$848$	−6.55554e9	−0.369167
$849$	1.55565e10	0.872437
$850$	−8.68260e9	−0.484935
$851$	1.68174e10	0.935418
$852$	−5.15950e9	−0.285805
$853$	2.33614e10	1.28877	0.644387	−	0.764699i	$-0.277112\pi$
$853$	2.33614e10	1.28877	0.644387	+	0.764699i	$0.277112\pi$
$854$	−1.14097e10	−0.626862
$855$	−7.02945e8	−0.0384627
$856$	8.61443e9	0.469427
$857$	−1.95953e9	−0.106346	−0.0531728	−	0.998585i	$-0.516933\pi$
$857$	−1.95953e9	−0.106346	−0.0531728	+	0.998585i	$0.516933\pi$
$858$	−5.69303e9	−0.307708
$859$	2.45197e10	1.31989	0.659947	−	0.751313i	$-0.270579\pi$
$859$	2.45197e10	1.31989	0.659947	+	0.751313i	$0.270579\pi$
$860$	1.45090e9	0.0777845
$861$	2.12368e9	0.113391
$862$	−2.28352e9	−0.121431
$863$	−7.33224e7	−0.00388328	−0.00194164	−	0.999998i	$-0.500618\pi$
$863$	−7.33224e7	−0.00388328	−0.00194164	+	0.999998i	$0.500618\pi$
$864$	6.44973e8	0.0340207
$865$	1.73250e8	0.00910156
$866$	−5.72663e9	−0.299631
$867$	5.71994e9	0.298074
$868$	−8.39759e9	−0.435849
$869$	4.40343e10	2.27626
$870$	−2.20646e8	−0.0113600
$871$	−9.23551e8	−0.0473584
$872$	1.07709e10	0.550102
$873$	3.12609e9	0.159020
$874$	1.53811e10	0.779289
$875$	−3.33691e9	−0.168390
$876$	4.55665e9	0.229024
$877$	2.32254e10	1.16269	0.581346	−	0.813656i	$-0.302526\pi$
$877$	2.32254e10	1.16269	0.581346	+	0.813656i	$0.302526\pi$
$878$	9.97882e9	0.497563
$879$	4.23816e9	0.210483
$880$	9.07223e8	0.0448771
$881$	−1.23809e10	−0.610012	−0.305006	−	0.952350i	$-0.598658\pi$
$881$	−1.23809e10	−0.610012	−0.305006	+	0.952350i	$0.598658\pi$
$882$	2.32682e9	0.114189
$883$	−1.66445e10	−0.813596	−0.406798	−	0.913518i	$-0.633355\pi$
$883$	−1.66445e10	−0.813596	−0.406798	+	0.913518i	$0.633355\pi$
$884$	3.54139e9	0.172421
$885$	−1.83025e8	−0.00887582
$886$	−2.66801e9	−0.128875
$887$	4.56813e9	0.219789	0.109895	−	0.993943i	$-0.464949\pi$
$887$	4.56813e9	0.219789	0.109895	+	0.993943i	$0.464949\pi$
$888$	3.53263e9	0.169298
$889$	6.16621e9	0.294349
$890$	−6.21739e8	−0.0295626
$891$	3.56631e9	0.168907
$892$	1.89979e10	0.896250
$893$	2.59160e10	1.21783
$894$	−4.45195e9	−0.208386
$895$	−1.41798e9	−0.0661135
$896$	−1.36648e9	−0.0634637
$897$	6.97886e9	0.322858
$898$	2.17233e10	1.00106
$899$	6.23239e9	0.286085
$900$	−3.59417e9	−0.164343
$901$	2.25485e10	1.02702
$902$	6.48046e9	0.294024
$903$	−1.20838e10	−0.546132
$904$	4.29582e9	0.193400
$905$	−3.44846e9	−0.154652
$906$	9.14831e9	0.408688
$907$	−2.78923e10	−1.24125	−0.620624	−	0.784108i	$-0.713121\pi$
$907$	−2.78923e10	−1.24125	−0.620624	+	0.784108i	$0.713121\pi$
$908$	−8.71998e9	−0.386558
$909$	−1.19308e10	−0.526862
$910$	6.75740e8	0.0297259
$911$	3.35606e9	0.147067	0.0735335	−	0.997293i	$-0.476572\pi$
$911$	3.35606e9	0.147067	0.0735335	+	0.997293i	$0.476572\pi$
$912$	3.23093e9	0.141041
$913$	1.22830e10	0.534141
$914$	−1.35814e9	−0.0588346
$915$	−1.95058e9	−0.0841765
$916$	1.33391e10	0.573447
$917$	1.46723e9	0.0628354
$918$	−2.21845e9	−0.0946455
$919$	3.55135e10	1.50935	0.754674	−	0.656100i	$-0.227795\pi$
$919$	3.55135e10	1.50935	0.754674	+	0.656100i	$0.227795\pi$
$920$	−1.11213e9	−0.0470866
$921$	−9.92356e9	−0.418561
$922$	1.36884e10	0.575168
$923$	−1.17271e10	−0.490890
$924$	−7.55581e9	−0.315086
$925$	−1.96859e10	−0.817823
$926$	−2.81715e10	−1.16593
$927$	1.32938e10	0.548113
$928$	1.01415e9	0.0416567
$929$	−2.67557e10	−1.09487	−0.547433	−	0.836850i	$-0.684395\pi$
$929$	−2.67557e10	−1.09487	−0.547433	+	0.836850i	$0.684395\pi$
$930$	−1.43564e9	−0.0585268
$931$	1.16560e10	0.473397
$932$	1.57072e10	0.635541
$933$	1.58694e10	0.639699
$934$	2.85939e10	1.14831
$935$	−3.12049e9	−0.124848
$936$	1.46596e9	0.0584330
$937$	2.25141e10	0.894060	0.447030	−	0.894519i	$-0.352482\pi$
$937$	2.25141e10	0.894060	0.447030	+	0.894519i	$0.352482\pi$
$938$	−1.22574e9	−0.0484940
$939$	−1.53920e10	−0.606687
$940$	−1.87385e9	−0.0735846
$941$	1.45437e10	0.568998	0.284499	−	0.958676i	$-0.408173\pi$
$941$	1.45437e10	0.568998	0.284499	+	0.958676i	$0.408173\pi$
$942$	−1.33698e10	−0.521132
$943$	−7.94414e9	−0.308500
$944$	8.41232e8	0.0325472
$945$	−4.23306e8	−0.0163171
$946$	−3.68741e10	−1.41613
$947$	5.03414e10	1.92620	0.963098	−	0.269152i	$-0.0867433\pi$
$947$	5.03414e10	1.92620	0.963098	+	0.269152i	$0.0867433\pi$
$948$	−1.13389e10	−0.432257
$949$	1.03569e10	0.393365
$950$	−1.80047e10	−0.681322
$951$	−1.42348e10	−0.536685
$952$	4.70015e9	0.176556
$953$	8.57358e9	0.320876	0.160438	−	0.987046i	$-0.448709\pi$
$953$	8.57358e9	0.320876	0.160438	+	0.987046i	$0.448709\pi$
$954$	9.33396e9	0.348054
$955$	−1.53598e9	−0.0570657
$956$	−1.72881e10	−0.639949
$957$	5.60765e9	0.206818
$958$	1.32465e10	0.486766
$959$	−7.29548e9	−0.267109
$960$	−2.33611e8	−0.00852206
$961$	1.30385e10	0.473911
$962$	8.02934e9	0.290782
$963$	−1.22655e10	−0.442580
$964$	−2.57509e10	−0.925813
$965$	−1.05611e9	−0.0378325
$966$	9.26237e9	0.330600
$967$	−4.75300e10	−1.69035	−0.845173	−	0.534494i	$-0.820502\pi$
$967$	−4.75300e10	−1.69035	−0.845173	+	0.534494i	$0.820502\pi$
$968$	−1.30793e10	−0.463470
$969$	−1.11131e10	−0.392376
$970$	−1.13228e9	−0.0398339
$971$	−3.46957e10	−1.21621	−0.608105	−	0.793856i	$-0.708070\pi$
$971$	−3.46957e10	−1.21621	−0.608105	+	0.793856i	$0.708070\pi$
$972$	−9.18330e8	−0.0320750
$973$	−1.35565e10	−0.471794
$974$	2.22221e10	0.770598
$975$	−8.16923e9	−0.282270
$976$	8.96542e9	0.308671
$977$	−5.63184e10	−1.93205	−0.966027	−	0.258442i	$-0.916791\pi$
$977$	−5.63184e10	−1.93205	−0.966027	+	0.258442i	$0.916791\pi$
$978$	−1.09246e10	−0.373440
$979$	1.58013e10	0.538211
$980$	−8.42784e8	−0.0286039
$981$	−1.53359e10	−0.518641
$982$	3.66179e10	1.23397
$983$	3.50106e10	1.17561	0.587804	−	0.809003i	$-0.299992\pi$
$983$	3.50106e10	1.17561	0.587804	+	0.809003i	$0.299992\pi$
$984$	−1.66873e9	−0.0558345
$985$	−3.20571e9	−0.106880
$986$	−3.48828e9	−0.115889
$987$	1.56064e10	0.516644
$988$	7.34361e9	0.242248
$989$	4.52025e10	1.48585
$990$	−1.29173e9	−0.0423106
$991$	3.42417e10	1.11763	0.558814	−	0.829293i	$-0.311257\pi$
$991$	3.42417e10	1.11763	0.558814	+	0.829293i	$0.311257\pi$
$992$	6.59859e9	0.214615
$993$	−6.78141e9	−0.219785
$994$	−1.55642e10	−0.502661
$995$	−2.58638e9	−0.0832360
$996$	−3.16288e9	−0.101432
$997$	3.86774e10	1.23602	0.618008	−	0.786172i	$-0.287940\pi$
$997$	3.86774e10	1.23602	0.618008	+	0.786172i	$0.287940\pi$
$998$	1.50258e10	0.478500
$999$	−5.02985e9	−0.159616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.e.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.e.1.5	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +33.0058 q^{5} +216.000 q^{6} +651.589 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +33.0058 q^{5} +216.000 q^{6} +651.589 q^{7} -512.000 q^{8} +729.000 q^{9} -264.046 q^{10} +6710.64 q^{11} -1728.00 q^{12} -3927.59 q^{13} -5212.71 q^{14} -891.156 q^{15} +4096.00 q^{16} -14088.6 q^{17} -5832.00 q^{18} -29214.8 q^{19} +2112.37 q^{20} -17592.9 q^{21} -53685.1 q^{22} +65810.5 q^{23} +13824.0 q^{24} -77035.6 q^{25} +31420.7 q^{26} -19683.0 q^{27} +41701.7 q^{28} -30949.5 q^{29} +7129.25 q^{30} -201373. q^{31} -32768.0 q^{32} -181187. q^{33} +112709. q^{34} +21506.2 q^{35} +46656.0 q^{36} +255543. q^{37} +233719. q^{38} +106045. q^{39} -16899.0 q^{40} -120712. q^{41} +140743. q^{42} +686859. q^{43} +429481. q^{44} +24061.2 q^{45} -526484. q^{46} -887083. q^{47} -110592. q^{48} -398975. q^{49} +616285. q^{50} +380393. q^{51} -251366. q^{52} -1.60047e6 q^{53} +157464. q^{54} +221490. q^{55} -333613. q^{56} +788801. q^{57} +247596. q^{58} +205379. q^{59} -57034.0 q^{60} +2.18882e6 q^{61} +1.61098e6 q^{62} +475008. q^{63} +262144. q^{64} -129633. q^{65} +1.44950e6 q^{66} +235145. q^{67} -901671. q^{68} -1.77688e6 q^{69} -172050. q^{70} +2.98582e6 q^{71} -373248. q^{72} -2.63695e6 q^{73} -2.04434e6 q^{74} +2.07996e6 q^{75} -1.86975e6 q^{76} +4.37258e6 q^{77} -848359. q^{78} +6.56186e6 q^{79} +135192. q^{80} +531441. q^{81} +965699. q^{82} +1.83037e6 q^{83} -1.12594e6 q^{84} -465006. q^{85} -5.49487e6 q^{86} +835635. q^{87} -3.43585e6 q^{88} +2.35466e6 q^{89} -192490. q^{90} -2.55917e6 q^{91} +4.21187e6 q^{92} +5.43707e6 q^{93} +7.09666e6 q^{94} -964259. q^{95} +884736. q^{96} +4.28818e6 q^{97} +3.19180e6 q^{98} +4.89206e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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